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Leonardo da Vinci's tree rule may be explained by wind (phys.org)
93 points by ColinWright 7 days ago | hide | past | web | favorite | 34 comments





Also pertinent to wind resistance is whether or not the tree is deciduous, the shape of the leaves' margin, the texture of bark and how they interact as a group in forests.

Another aspect that explains why the vascular explanation is not enough is the resistance of the trunk in supporting the wood's weight. Also important here is the roots' structure.

When I imagine a situation where wind resistance is fundamental, I think of palm trees being subject to seasonal tropical storms, and these look nothing like the diagram in the article.

Underwater, where vascularization and weight are not as important to many branching structures like corals or algae, there is still the problem of resistance against a moving fluid. But the branching/girth/length/angle rules seem to be different.

So I'm still with team "branching optimized for sun/air exposure and constrained by vascularization, weight and root structure".


Just a note - palm trees are part of the grass family, and have more in common with bamboo and turf grass than they do with trees. It doesn't surprise me that they would be different.

Exactly. And here is the point: what exactly does 'tree' mean here?

Palm trees, bamboo, corn, reeds and such are all of them quite different from the schema presented in the article. This schema seems to be some specific subset of large Eudicots, like magnolias, oaks, shrubs and such, or at any rate some paraphyletic family of plants.

In taxonomical terms, Pinophyta are even more distant from the aforementioned plants, all of them Magnoliophyta. Pine trees, cypresses and other Pinophyta branch as well, but their branching does not fit the schema in the article.

Why wasn't the hypothesis tested against the Pinophytae' specific (and quite common) kind of branching? Is surrounding fluid resistance only important for that arbitrary set of plants?

If fluid resistance, ubiquitous in plant evolution, were of such an importance in explaining a difference between what is predicted by the vascular hypothesis and what is actually observed in branching trees, the same could be said for all trees that branch, and this theory should be able to do some predictions for other branching (and non-branching) plants.

This hypothesis should have been tested for other structures right from the start, and not just for an idealized form of unwarranted generality.

But don't get me wrong: I think that it's very good to have aerospace engineers putting forth this idea, and this article adds to our understanding of tree growth and evolution. I just find it incomplete.


Most plants would be protected by trees, so trees kinda ... stand out.

It occurs to me this could be a metaphor for code complexity at various levels of abstraction. I'm picturing a recursive method that:

- calculates LOC of a top-level method - calculates lines of code for each method called within that - builds an hourglass visualization showing as you go up or down the abstraction layers how the LOC changes

It seems like this might be useful for seeing - where in the abstraction layers there are major changes in density of functions - where there is over-abstraction (many, many tiny functions) - where there is not enough abstraction (a bulge in LOC, or overall large numbers)

Combining this with cyclomatic complexity may provide a more nuanced view for code analysis. It would allow you to quickly hone in on parts of the code-base that have too much density.


> the combined cross-sectional areas of a tree’s daughter branches are equal to the cross-sectional area of the mother branch.

Seems so logical, for a flow in the daughter pipes to match the mother pipe... except that the wood of a tree is dead, and the flow happens in the bark... leading to a sum-rule for circumference, proportional to radii and diameter.

However, the point of a tree is structural, to get higher than other trees, higher than herbivores. Is the strength of wood proportional to cross-sectional area (required to resist gravity - the essential problem of height)? If so, that would explain the rule. Similar reasoning to wind in the article.

EDIT it also means the weight per height remains constant through branching... this doesn't seem sustainable; you'd want it to taper.


I like your train of thought. You absolutely want the right amount of taper.

Regarding wood strength being proportional to area: it can't be as simple as that - wood is a strongly anisotropic material, so direction of loading becomes critical to understanding what's going on.

Natural trees have defects, and they "know" it. Limb attachment is messy business - in many species they are frequently defective. Doesn't reduce well to modeling actual limbs as simple beams or whatnot.

Starting to understand thigmomorphogenesis and how trees deal with it in terms of load shedding, compartmentalization, and reaction wood growth was one of my favorite "ahhh ha" moments.


They do taper, the method is to drop branches and limbs over time. Look at an old tree and the first branch is often 10+ feet above the ground, where young trees have many branches much lower.

It's surprising for me that this is new idea. Wind is the main thing trees oppose (besides gravity and each other). It should be first idea that this is the thing that shapes them.

This might be one of the cases when weird experimental "law" drives people away from the actual cause.

I always felt the same way about Kepler's laws. While they are true, you can't find in them any trace of actual reason why things are the way they are (conservation of energy and angular momentum in gravity field).


It's definitely not a new idea. The idea that trees maintain strength by equalizing stress throughout their structure is a classic one.

Angiosperms depends on tensile stresses for their strength. Trees keeping themselves upright is all about carefully distributing compressive and tensile strength in response to the environment.

Claus Mattheck's books cover this in detail.


> While they are true, you can't find in them any trace of actual reason why things are the way they are (conservation of energy and angular momentum in gravity field).

Your so-called "causes" seem just to be more general "experimental laws". Does conservation of energy really make you feel like you understand the reason why things are the way they are?


> Does conservation of energy really make you feel like you understand the reason why things are the way they are?

Yes. Definitely. Definitely more than "The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit."

One sounds like a rule of nature, the other sounds like semi-accidental math gimmick.


If I told you that your car was propelled by an engine that ran on gasoline, would you feel any closer to understanding it?

No, because that's profoundly misleading. The car is propelled by the wheels. Those may be moved by a motor directly or indirectly, but the car is not moved forward by the explosion of gas directly, there needs to be a transformation of the energy into circular motion. There are many many different types of motor, so the specifics may be detailed. But for a naive explanation, you could just say "fire".

I wonder how difficult it is to build wooden axis and hinges that overcome the force of friction in old carts.


> Wind is the main thing trees oppose (besides gravity and each other). It should be first idea that this is the thing that shapes them.

This statement was unexpectedly profound.


Why should this have anything to do with wind. It would seem to me that he conservation of cross sectional area is because all the capillaries need to go from root to leaf.

If the area above a branching point was more than below then how would those capillaries going up to the leaves be fed?

If the area above a branching point were less than blow then how would the capillaries going down to the roots be fed?

Remember the roots fees the leaves and the leaves feed the roots. So it needs to be a balanced system.


From the article

Although researchers have previously proposed explanations for the rule based on hydraulics or structure, none of these explanations have been fully convincing. For instance, the hydraulic explanation called the “pipe model” proposes that the branching proportions have to do with the way that vascular vessels connect the tree’s roots to its leaves to provide water and nutrients. But since vascular vessels account for as little as 5% of the branch cross section (for large trunks in some tree species), it seems unlikely that they would govern the tree’s entire architecture.


Is there variation in areas where the winds are low compared to where they are high?

Monterrey pine grown in it's natural costal habitat is gnarly and unsuitable for lumber. The same tree grown on plantations outside the US produces straight grained "radiata" pine lumber.

Am I correct in assuming that the natural coastal habitat is windier than the plantations?

I find the article and paper somewhat frustrating.

It doesn't say anything new about da Vinci, and it sure doesn't seem to add anything which isn't already an accepted idea in biomechanics. The article revives vascular constraints as a strawman before beating it down again, as if it's still a theory of limb structure thats taken seriously.

My takeaway: da Vinci's rule is easily explained by modern foundational biomechanics.


What's the beat-down?

Amazing that someone 500 years ago was both interested in and had the analytical skills to propose a rule we are still trying to understand today.

.. and that "Someone" was nearly always the same guy: Leonardo da Vinci. He must have been maybe the most curious man ever.

A few notes:

* 500 years ago there hadn’t been intensive centuries-long studies of many of these phenomena, so if you wanted to know something about it the only way was to do independent investigation.

* Even for subjects which had been studied, books were rare/expensive, poorly indexed, often contained a mishmash of disorganized material, hard to track down, and often flagrantly wrong but remaining uncorrected for centuries.

* Leonardo was notoriously bad at sticking with any project, from his childhood on, easily abandoning his work and jumping to another topic, including leaving many of his paid projects unfinished. Probably serious ADHD.

* There have been many intensely curious polymaths, but in many cases they didn’t take proper notes, the notes were lost/destroyed, the notes are buried in an archive somewhere where nobody reads about them, ...


If you'd imagine the growth somewhat like a material paste, if the material flow is constant and if the branches grow with equal length, then da Vincis rule follows, no matter the individual branch girth. I suspect da Vinci wasn't observing this as much as arriving how it ought to be.

Gravity and wind. Wind alone doesn't explain it.

I would have just assumed 'divide by two' was the most likely genetic accident to fall into place and it worked fine.

I thought this had been explained by how this setup maximizes the efficiency of the respiratory system.

This was discussed in a great book I read called Scale:

https://www.amazon.com/Scale-Universal-Growth-Organisms-Comp...

the human vascular system follows the same rule iirc.


Shouldn’t that be in reverse? I’m pretty sure Wind came before da Vinci

That website almost freezes Firefox for me after a couple of seconds.

And I cannot do a JavaScript profile as it just locks everything...


Curious that your experience of the site is radically different from mine. For me it loads quickly and is perfectly responsive.

Firefox 62.0.3 (64-bit) on Ubuntu 14.04.


I experience the same on FF 62.0.3 MacOS. Running uBlock and uMatrix and some other add-ons so I think there might be some less then stellar first party js to blame.

Also using those. Weird!



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